Machine Learning, Dynamical Systems and Control

Reduced order models (ROMs) aim to exploit underlying, low-dimensional patterns of spatio-temporal activity in order to promote improved understanding of the systems as well as computational efficiency. Critical to the successful implementation of a reduced order model scheme is the ability to interpolate the nonlinear contributions to the dynamical evolution. This was recognized early in ROM computational schemes and a suite of methods, broadly termed gappy POD methods, have been developed in order to provide interpolation methodologies for producing efficient, low-dimensional ROMs.

 

Section 12.1: Gappy POD

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Section 12.2: Error and Convergence of Gappy POD

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Section 12.3: Gappy Measurements: Minimize Condition Number

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Section 12.4: Gappy Measurements: Maximal Variance

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Section 12.5: POD and the Discrete Empirical Interpolation Method

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Section 12.6: ROMs with DEIM Implementation

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Section 12.7: Machine Learning ROMs

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